Managing your family:
With the bloodline traits, you can keep track of your entire noble family with ease. However, it is easy for small families like Arryn or Stannis to dwindle and die off. The tip to keep your blood pure is obviously, never adopt. Also, some factions start off with no heir, so some generals are designated as heir. However, once you raised your own garden (as Lord Tywin puts it) you know what must be done to secure the throne for your own kin.
Managing armies and battles:
If you don't have experience with RealCombat, it's a unit balancing mod that emphasizes the importance of armored units. In vanilla, armor-clad knights die as easily as lowly peasants wearing boiled leather. In RC, a well-trained armored unit can stand up to peasants three times its number, and only be worn down by fatigue. Have no fear of imba however, for a well aimed cavalry can spell doom to the best armored knights on foot. But lowly spear-wielding peasants can slow down an armored charge long enough to bring your own forces to bear. In short, RC achived a much more tactical-inclined balance than vanilla. Combined-arms stacks are highly encouraged, and you could decide between expensive, hard to replenish elites vs commoner levies that are cheap and easy to mass.
Most settlements have a heraldic anc which generals can acquire by staying in the town for one turn. For example, If you conquer Harrenhal and sit Ser Gregor inside, he'll be granted the title Lord of Harrenhal as an ancillary. The only exception are the capital settlements of each family, whose heraldry is automatically granted to the current faction leader. For example, if Tywin dies and Kevan becomes leader, he'll be automatically granted the Lord of Casterly Rock, without having to stay there one turn.
Each noble house has two basic offices to grant to generals or family members: Castellan and Master of Horse. Each King has the right to grant several additional offices to serve as his council: Hand of King, Master of Coin, Master of Ship, and Master of Law. Here's how you acquire these offices: (All of them require your general to stay inside a settlement)
Castellan: Stay in Capital, have more than 4 loyalty
Master of Horse: Train cavalry
Hand: have more than 2 authority
Law: Keep your townsfolks happy
Coin: Tax your town
Ship: Build a ship
Crowns and Ancillaries in general:
Watch out how many ancs your faction lead has when he claims king. The hardcoded max number of ancillaries per general is eight, so if he already has eight ancs, he won't get a crown. Some ancillaries are transferable, such as offices and heraldries, you could keep a few on your heirs and leaders to save spare ancillary space.
Regarding the advisor optional events:
Don't save in the middle of one, it won't pop up again when you reload.
Watch out where you're standing when you're spawning anything (assassins usually), keep the space around your capital's ports clear or you will be declined by the guilds.
If you have any more questions regarding gameplay, I'll add stuff to this section later.